Functional composition algorithms via blossoming

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions <italic>F</italic> and <italic>G</italic>, compute a representation of the function <italic>H</italic> = <italic>F o G</italic>. We examine this problem in detail for the case when <italic>F</italic> and <italic>G</italic> are given in either Be´zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.

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